[Astrodude]

I'm trying to write a function that outputs that Taylor series sum of the sine of an angle and it's only working for 0 and 90 degrees and no other values.

int factorial(int n)
{
      int i; 
      int f;
       
      for(i=0; i<=n; i++)
      {
          if(i==0){
			  f=1;
		  }
		  else{

		  f = f * i;
		  }
      }
       
      return(f);  
}
double sind(double angle){
	double r;
	int n;
	int sum;
	int term;
	r=(PI/180)*angle;
	sum=r;
	term=r;
	n=3;
	while(term>=0.0001){
			term=(r*r*term)/factorial(n)*(-1);
			sum=sum+term;
			n+=2;
		}
	return(sum);
}

[Lux Perpetua]

sin(r) = r - r^3/6 + r^5/120 - r^7/5040 + ...
= r + r*(-r*r/(2*3)) + r*(-r*r/(2*3))*(-r*r/(4*5)) + r*(-r*r/(2*3))*(-r*r/(4*5))*(-r*r/(6*7)) + ...

so this is wrong:

			term=(r*r*term)/factorial(n)*(-1);

[Astrodude]

Originally Posted by Lux Perpetua

sin(r) = r - r^3/6 + r^5/120 - r^7/5040 + ...
= r + r*(-r*r/(2*3)) + r*(-r*r/(2*3))*(-r*r/(4*5)) + r*(-r*r/(2*3))*(-r*r/(4*5))*(-r*r/(6*7)) + ...

so this is wrong:

			term=(r*r*term)/factorial(n)*(-1);

I can't find the mistake in my code. How is that term wrong when n increments 2?

I've updated my code.

int factorial(int n)
{
      int i; 
      int f;
       
      for(i=0; i<=n; i++)
      {
          if(i==0){
			  f=1;
		  }
		  else{

		  f = f * i;
		  }
      }
       
      return(f);  
}
double sind(double angle){
	double r;
	int n;
	int sum;
	int term;
	int Taylor;
	r=(PI/180)*angle;
	sum=r;
	term=r;
	Taylor=r;
	n=3;
	while(Taylor>=ALMOSTZERO){
			
			term=(r*r*term)*-1;
			Taylor=term/factorial(n);
			sum=sum+Taylor;
			n+=2;
		}
	return(sum);
}

[bdb]

When you convert an angle to radians

r=(PI/180)*angle;

and then, that value to int

Taylor=r;

you will always get 0 for angles in the range 0 to 57.2957795...
1 for angles in the range 57.3 to 114.6
...

[Astrodude]

Originally Posted by bdb

When you convert an angle to radians

r=(PI/180)*angle;

and then, that value to int

Taylor=r;

you will always get 0 for angles in the range 0 to 57.2957795...
1 for angles in the range 57.3 to 114.6
...

Thanks for the help! The program works a lot better now that I've switched those terms to doubles!

It's still not giving accurate outputs though; frequently off after the first decimal place. I thought the Taylor term was redundant so I got rid of it.

Here's the code:

int factorial(int n)
{
      int i; 
      int f;
       
      for(i=0; i<=n; i++)
      {
          if(i==0){
			  f=1;
		  }
		  else{

		  f = f * i;
		  }
      }
       
      return(f);  
}
double sind(double angle){
	double r;
	int n;
	double sum;
	double term;
	r=(PI/180)*angle;
	sum=r;
	term=r;
	n=3;
	while(term>=0.00001){
			term=(r*r*term)/factorial(n)*(-1);
			sum+=term;
			n+=2;
		}
	return(sum);
}

The output is still slightly off.

[bdb]

term is either positive or negative.
When it is negative your while loop terminates

[Astrodude]

Originally Posted by bdb

term is either positive or negative.
When it is negative your while loop terminates

I've actually changed it to be:

while(abs(term)>=ALMOSTZERO)){
			term=(r*r*term)/factorial(n)*(-1);
			sum+=term;
			n+=2;
		}

and I'm getting the same output. The sine of 30 degrees is 0.4997 according to my program.

[bdb]

I think maybe you want fabs() (declared in <math.h>) ... abs() (declared in <stdlib.h>) accepts and returns values of type int.

[Astrodude]

Originally Posted by bdb

I think maybe you want fabs() (declared in <math.h>) ... abs() (declared in <stdlib.h>) accepts and returns values of type int.

I switched to fabs and I got the same results.

[Lux Perpetua]

Originally Posted by Astrodude

I can't find the mistake in my code. How is that term wrong when n increments 2?

Write out the first few terms in your version with actual numbers. Print the terms out in your program to verify that they agree with what you wrote out. You will see that your terms are not the same as my terms. Hint: your denominator is wrong.

[Astrodude]

Originally Posted by Lux Perpetua

Write out the first few terms in your version with actual numbers. Print the terms out in your program to verify that they agree with what you wrote out. You will see that your terms are not the same as my terms. Hint: your denominator is wrong.

Ah thanks! Now I get what you were saying. I was multiplying factorials together in my program before. I've fixed it and it works.